Sobolev Regularity for the Bergman Projection on Relatively Compact Domains in Hermitian Manifolds

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2025年2月21日

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Phillip S. Harrington

摘要

Generalizing a result of Berndtsson and Charpentier, we provide sufficient conditions for $L^2$ $L^{2}$ Sobolev regularity of the Bergman projection acting on $L^2$ $L^{2}$ sections of a holomorphic line bundle restricted to a relatively compact domain with Lipschitz boundary in a Hermitian manifold. We provide examples to show that our methods work for domains in Hopf manifolds endowed with a suitable Hermitian metric.